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Write an equation and solve. Jeff can wash and wax his car in 3 hours, but his dad can do it in only 2 hours. How long will it take the two of them to wash and wax together?

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Answer to a math question Write an equation and solve. Jeff can wash and wax his car in 3 hours, but his dad can do it in only 2 hours. How long will it take the two of them to wash and wax together?

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Cristian
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117 Answers
Let's denote the time it takes for Jeff to wash and wax the car as x hours and the time it takes for his dad to wash and wax the car as y hours.

Jeff can do the job in 3 hours, so his work rate is \frac{1}{3} of the car per hour.
Similarly, Jeff's dad can do the job in 2 hours, so his work rate is \frac{1}{2} of the car per hour.

When they work together, their work rates are combined, so the equation becomes:
\frac{1}{3} + \frac{1}{2} = \frac{1}{x} + \frac{1}{y}

To solve for x and y , we notice that Jeff and his dad are working on the same job, the time taken when working together is the same, so:
\frac{1}{x} + \frac{1}{y} = \frac{1}{3} + \frac{1}{2} = \frac{5}{6}

Now, we need to find the time for both of them to complete the job together, which is the reciprocal of the combined work rate:
x = y = \frac{1}{\frac{5}{6}} = \frac{6}{5} \text{ hours}

Therefore, it will take Jeff and his dad \frac{6}{5} hours to wash and wax the car together.

\boxed{\frac{6}{5}\text{ or 1.2 hours}}

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